Police were called to BP Garage in New Street at 3.40am on Tuesday, September 5.
It was reported that a man wearing a face covering had threatened a member of staff with a screwdriver before stealing two bottles of Ciroc vodka.
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The member of staff suffered a small cut to his neck during the incident.
The man then left and went along New Street past McDonald’s.
At 8.11am the same morning, officers were alerted to an incident in the neighbouring McDonald’s, where a man was reported to have gone behind the tills and walked around the kitchen.
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He then ran away following a brief altercation with a staff member and the two incidents are being treated as linked.
Now a 19-year-old man from Bournemouth has been arrested on suspicion of common assault and aggravated burglary.
A police spokesperson said: “He has been released from custody on police bail as enquiries continue.”